Open this publication in new window or tab >>2014 (English)In: Discrete and Continuous Dynamical Systems, ISSN 1078-0947, E-ISSN 1553-5231, Vol. 34, no 2, p. 367-377Article in journal (Refereed) Published
Abstract [en]
In the paper, we obtain necessary and sufficient conditions for ergodicity (with respect to the normalized Haar measure) of discrete dynamical systems < f; S2-r (a)> on 2-adic spheres S2-r (a) of radius 2(-r), r >= 1, centered at some point a from the ultrametric space of 2-adic integers Z(2). The map f: Z(2) -> Z(2) is assumed to be non-expanding and measure-preserving; that is, f satisfies a Lipschitz condition with a constant 1 with respect to the 2-adic metric, and f preserves a natural probability measure on Z(2), the Haar measure mu(2) on Z(2) which is normalized so that mu(2)(Z(2)) = 1.
Keywords
Ergodic theory, 1-Lipschitz dynamics, 2-adic sphere, p-adic analysis
National Category
Mathematics
Research subject
Natural Science, Mathematics
Identifiers
urn:nbn:se:lnu:diva-30644 (URN)10.3934/dcds.2014.34.367 (DOI)000325646400002 ()2-s2.0-84885971608 (Scopus ID)
2013-11-222013-11-222017-12-06Bibliographically approved